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We present $k^{O(k^2)} m$ time algorithms for various problems about decomposing a given undirected graph by edge cuts or vertex separators of size $

In 1985, W.K.Hayman (Bayer. Akad. Wiss. Math.-Natur. Kl. Sitzungsber, 1984(1985), 1-13.) proved that there do not exist non-constant meromorphic functions $f,$ $g$ and $h$ satisfying the functional equation $f^n+g^n+h^n=1$ for $n\geq 9.$ We prove that there do not exist non-constant meromorphic solutions $f,$ $g,$ $h$ satisfying the functional equation $f^8+g^8+h^8=1.$ In 1971, N. Toda (T\^{o}hoku Math. J. 23(1971), no. 2, 289-299.) proved that there do not exist non-constant entire functions $f,$ $g,$ $h$ satisfying $f^n+g^n+h^n=1$ for $n\geq 7.$ We prove that there do not exist non-constant entire functions $f,$ $g,$ $h$ satisfying the functional equation $f^6+g^6+h^6=1.$ Our results answer questions of G. G. Gundersen., Comment: 40 pages. arXiv admin note: text overlap with arXiv:math/9310226 by other authors

Cycle packing is a fundamental problem in optimization, graph theory, and algorithms. Motivated by recent advancements in finding vertex-disjoint paths between a specified set of vertices that either minimize the total length of the paths [Bj\"orklund, Husfeldt, ICALP 2014; Mari, Mukherjee, Pilipczuk, and Sankowski, SODA 2024] or request the paths to be shortest [Lochet, SODA 2021], we consider the following cycle packing problems: Min-Sum Cycle Packing and Shortest Cycle Packing. In Min-Sum Cycle Packing, we try to find, in a weighted undirected graph, $k$ vertex-disjoint cycles of minimum total weight. Our first main result is an algorithm that, for any fixed $k$, solves the problem in polynomial time. We complement this result by establishing the W[1]-hardness of Min-Sum Cycle Packing parameterized by $k$. The same results hold for the version of the problem where the task is to find $k$ edge-disjoint cycles. Our second main result concerns Shortest Cycle Packing, which is a special case of Min-Sum Cycle Packing that asks to find a packing of $k$ shortest cycles in a graph. We prove this problem to be fixed-parameter tractable (FPT) when parameterized by $k$ on weighted planar graphs. We also obtain a polynomial kernel for the edge-disjoint variant of the problem on planar graphs. Deciding whether Min-Sum Cycle Packing is FPT on planar graphs and whether Shortest Cycle Packing is FPT on general graphs remain challenging open questions.

In the Hedge Cut problem, the edges of a graph are partitioned into groups called hedges, and the question is what is the minimum number of hedges to delete to disconnect the graph. Ghaffari, Karger, and Panigrahi [SODA 2017] showed that Hedge Cut can be solved in quasipolynomial-time, raising the hope for a polynomial time algorithm. Jaffke, Lima, Masar\'ik, Pilipczuk, and Souza [SODA 2023] complemented this result by showing that assuming the Exponential Time Hypothesis (ETH), no polynomial-time algorithm exists. In this paper, we show that Hedge Cut is fixed-parameter tractable parameterized by the solution size $\ell$ by providing an algorithm with running time $\binom{O(\log n) + \ell}{\ell} \cdot m^{O(1)}$, which can be upper bounded by $c^{\ell} \cdot (n+m)^{O(1)}$ for any constant $c>1$. This running time captures at the same time the fact that the problem is quasipolynomial-time solvable, and that it is fixed-parameter tractable parameterized by $\ell$. We further generalize this algorithm to an algorithm with running time $\binom{O(k \log n) + \ell}{\ell} \cdot n^{O(k)} \cdot m^{O(1)}$ for Hedge $k$-Cut., Comment: 12 pages, 1 figure, to appear in SODA 2025

The properties of functional brain networks are heavily influenced by how the network nodes are defined. A common approach uses Regions of Interest (ROIs), which are predetermined collections of fMRI measurement voxels, as network nodes. Their definition is always a compromise, as static ROIs cannot capture the dynamics and the temporal reconfigurations of the brain areas. Consequently, the ROIs do not align with the functionally homogeneous regions, which can explain the very low functional homogeneity values observed for the ROIs. This is in violation of the underlying homogeneity assumption in functional brain network analysis pipelines and it can cause serious problems such as spurious network structure. We introduce the node-reconfiguring multilayer network model, where nodes represent ROIs with boundaries optimized for high functional homogeneity in each time window. In this representation, network layers correspond to time windows, intralayer links depict functional connectivity between ROIs, and interlayer link weights quantify overlap between ROIs on different layers. The ROI optimization approach increases functional homogeneity notably, yielding an over 10-fold increase in the fraction of ROIs with high homogeneity compared to static ROIs from the Brainnetome atlas. The optimized ROIs reorganize non-trivially at short time scales of consecutive time windows and across several windows. The amount of reorganization across time windows is connected to intralayer hubness: ROIs that show intermediate levels of reorganization have stronger intralayer links than extremely stable or unstable ROIs. Our results demonstrate that reconfiguring parcellations yield more accurate network models of brain function. This supports the ongoing paradigm shift towards the chronnectome that sees the brain as a set of sources with continuously reconfiguring spatial and connectivity profiles., Comment: 23+6 pages, 8+4 figures

Let $G$ be the finite simple group of Lie type $G = E_7(q)$, where $q$ is an odd prime power. Then $G$ is an index $2$ subgroup of the adjoint group $G_{\operatorname{ad}}$, which is also denoted by $G_{\operatorname{ad}} = \operatorname{Inndiag}(G)$ and known as the group of inner-diagonal automorphisms. It was proven by Cohen--Liebeck--Saxl--Seitz (1992) that there is an elementary abelian $2$-subgroup $E$ of order $4$ in $G_{\operatorname{ad}}$, such that $N_{G_{\operatorname{ad}}}(E)/C_{G_{ad}}(E) \cong \operatorname{Sym}_3$, and $C_{G_{\operatorname{ad}}}(E) = E \times \operatorname{Inndiag}(D_4(q))$. Furthermore, such an $E$ is unique up to conjugacy in $G_{\operatorname{ad}}$. It is known that $N_G(E)$ is always a maximal subgroup of $G$, and $N_{G_{\operatorname{ad}}}(E)$ is a maximal subgroup of $G_{\operatorname{ad}}$ unless $N_{G_{\operatorname{ad}}}(E) \leq G$. In this note, we describe the structure of $N_{G}(E)$. It turns out that $N_G(E) = N_{G_{\operatorname{ad}}}(E)$ if and only if $q \equiv \pm 1 \mod{8}$., Comment: 9 pages

Instruction tuning enhances large language models (LLMs) by aligning them with human preferences across diverse tasks. Traditional approaches to create instruction tuning datasets face serious challenges for low-resource languages due to their dependence on data annotation. This work introduces a novel method, Multilingual Reverse Instructions (MURI), which generates high-quality instruction tuning datasets for low-resource languages without requiring human annotators or pre-existing multilingual models. Utilizing reverse instructions and a translation pipeline, MURI produces instruction-output pairs from existing human-written texts in low-resource languages. This method ensures cultural relevance and diversity by sourcing texts from different native domains and applying filters to eliminate inappropriate content. Our dataset, MURI-IT, includes more than 2 million instruction-output pairs across 200 languages. Evaluation by native speakers and fine-tuning experiments with mT5 models demonstrate the approach's effectiveness for both NLU and open-ended generation. We publicly release datasets and models at https://github.com/akoksal/muri.

Achieving high-precision measurements on near-term quantum devices is critical for advancing quantum computing applications. In this paper, we explore several practical techniques to enhance measurement accuracy using randomized measurements, focusing on minimizing shot overhead, circuit overhead, measurement noise, and time-dependent measurement noise. Our approach leverages locally biased random measurements to reduce shot overhead, in addition to repeated settings and parallel quantum detector tomography to reduce circuit overhead and mitigate measurement noise. Additionally, we employ a blended scheduling technique to mitigate time-dependent measurement noise. We demonstrate the effectiveness of these techniques through a case study on the molecular energy estimation of the BODIPY molecule using the Hartree-Fock state on an IBM Eagle r3 computer, showcasing significant improvements in measurement precision. These strategies pave the way for more reliable and accurate quantum computations, particularly in applications requiring precise molecular energy calculations., Comment: 15 pages, 8 figures

Traditional benchmarking in NLP typically involves using static held-out test sets. However, this approach often results in an overestimation of performance and lacks the ability to offer comprehensive, interpretable, and dynamic assessments of NLP models. Recently, works like DynaBench (Kiela et al., 2021) and CheckList (Ribeiro et al., 2020) have addressed these limitations through behavioral testing of NLP models with test types generated by a multistep human-annotated pipeline. Unfortunately, manually creating a variety of test types requires much human labor, often at prohibitive cost. In this work, we propose SYNTHEVAL, a hybrid behavioral testing framework that leverages large language models (LLMs) to generate a wide range of test types for a comprehensive evaluation of NLP models. SYNTHEVAL first generates sentences via LLMs using controlled generation, and then identifies challenging examples by comparing the predictions made by LLMs with task-specific NLP models. In the last stage, human experts investigate the challenging examples, manually design templates, and identify the types of failures the taskspecific models consistently exhibit. We apply SYNTHEVAL to two classification tasks, sentiment analysis and toxic language detection, and show that our framework is effective in identifying weaknesses of strong models on these tasks. We share our code in https://github.com/Loreley99/SynthEval_CheckList., Comment: EMNLP 2024 - Findings

Developing imaging models capable of detecting pathologies from chest X-rays can be cost and time-prohibitive for large datasets as it requires supervision to attain state-of-the-art performance. Instead, labels extracted from radiology reports may serve as distant supervision since these are routinely generated as part of clinical practice. Despite their widespread use, current rule-based methods for label extraction rely on extensive rule sets that are limited in their robustness to syntactic variability. To alleviate these limitations, we introduce RadPert, a rule-based system that integrates an uncertainty-aware information schema with a streamlined set of rules, enhancing performance. Additionally, we have developed RadPrompt, a multi-turn prompting strategy that leverages RadPert to bolster the zero-shot predictive capabilities of large language models, achieving a statistically significant improvement in weighted average F1 score over GPT-4 Turbo. Most notably, RadPrompt surpasses both its underlying models, showcasing the synergistic potential of LLMs with rule-based models. We have evaluated our methods on two English Corpora: the MIMIC-CXR gold-standard test set and a gold-standard dataset collected from the Cambridge University Hospitals., Comment: Accepted at BioNLP, ACL 2024

We propose an application of online hard sample mining for efficient training of Neural Radiance Fields (NeRF). NeRF models produce state-of-the-art quality for many 3D reconstruction and rendering tasks but require substantial computational resources. The encoding of the scene information within the NeRF network parameters necessitates stochastic sampling. We observe that during the training, a major part of the compute time and memory usage is spent on processing already learnt samples, which no longer affect the model update significantly. We identify the backward pass on the stochastic samples as the computational bottleneck during the optimization. We thus perform the first forward pass in inference mode as a relatively low-cost search for hard samples. This is followed by building the computational graph and updating the NeRF network parameters using only the hard samples. To demonstrate the effectiveness of the proposed approach, we apply our method to Instant-NGP, resulting in significant improvements of the view-synthesis quality over the baseline (1 dB improvement on average per training time, or 2x speedup to reach the same PSNR level) along with approx. 40% memory savings coming from using only the hard samples to build the computational graph. As our method only interfaces with the network module, we expect it to be widely applicable.

The first generation of ELT instruments includes an optical-infrared high-resolution spectrograph, indicated as ELT-HIRES and recently christened ANDES (ArmazoNes high Dispersion Echelle Spectrograph). ANDES consists of three fibre-fed spectrographs ([U]BV, RIZ, YJH) providing a spectral resolution of $\sim$100,000 with a minimum simultaneous wavelength coverage of 0.4-1.8 $\mu$m with the goal of extending it to 0.35-2.4 $\mu$m with the addition of a U arm to the BV spectrograph and a separate K band spectrograph. It operates both in seeing- and diffraction-limited conditions and the fibre feeding allows several, interchangeable observing modes including a single conjugated adaptive optics module and a small diffraction-limited integral field unit in the NIR. Modularity and fibre-feeding allow ANDES to be placed partly on the ELT Nasmyth platform and partly in the Coud\'e room. ANDES has a wide range of groundbreaking science cases spanning nearly all areas of research in astrophysics and even fundamental physics. Among the top science cases, there are the detection of biosignatures from exoplanet atmospheres, finding the fingerprints of the first generation of stars, tests on the stability of Nature's fundamental couplings, and the direct detection of the cosmic acceleration. The ANDES project is carried forward by a large international consortium, composed of 35 Institutes from 13 countries, forming a team of almost 300 scientists and engineers which include the majority of the scientific and technical expertise in the field that can be found in ESO member states., Comment: SPIE astronomical telescope and instrumentation 2024, in press

Multiple choice question answering tasks evaluate the reasoning, comprehension, and mathematical abilities of Large Language Models (LLMs). While existing benchmarks employ automatic translation for multilingual evaluation, this approach is error-prone and potentially introduces culturally biased questions, especially in social sciences. We introduce the first multitask, multiple-choice Turkish QA benchmark, TurkishMMLU, to evaluate LLMs' understanding of the Turkish language. TurkishMMLU includes over 10,000 questions, covering 9 different subjects from Turkish high-school education curricula. These questions are written by curriculum experts, suitable for the high-school curricula in Turkey, covering subjects ranging from natural sciences and math questions to more culturally representative topics such as Turkish Literature and the history of the Turkish Republic. We evaluate over 20 LLMs, including multilingual open-source (e.g., Gemma, Llama, MT5), closed-source (GPT 4o, Claude, Gemini), and Turkish-adapted (e.g., Trendyol) models. We provide an extensive evaluation, including zero-shot and few-shot evaluation of LLMs, chain-of-thought reasoning, and question difficulty analysis along with model performance. We provide an in-depth analysis of the Turkish capabilities and limitations of current LLMs to provide insights for future LLMs for the Turkish language. We publicly release our code for the dataset and evaluation: https://github.com/ArdaYueksel/TurkishMMLU., Comment: EMNLP 2024 - Findings

Context. High frame-rate imaging was employed to mitigate the effects of atmospheric turbulence (seeing) in observations of globular cluster Terzan 5. Aims. High-precision time-series photometry has been obtained with the highest angular resolution so far taken in the crowded central region of Terzan 5, with ground-based telescopes, and ways to avoid saturation of the brightest stars in the field observed. Methods. The Electron-Multiplying Charge Coupled Device (EMCCD) camera installed at the Danish 1.54-m telescope at the ESO La Silla Observatory was employed to produce thousands of short-exposure time images (ten images per second) that were stacked to produce the normal-exposure-time images (minutes). We employed difference image analysis in the stacked images to produce high-precision photometry using the DanDIA pipeline. Results. Light curves of 1670 stars with 242 epochs were analyzed in the crowded central region of Terzan 5 to statistically detect variable stars in the field observed. We present a possible visual counterpart outburst at the position of the pulsar J1748-2446N, and the visual counterpart light curve of the low-mass X-ray binary CX 3. Additionally, we present the discovery of 4 semiregular variables. We also present updated ephemerides and properties of the only RR Lyrae star previously known in the field covered by our observations in Terzan 5. Finally, we report a significant displacement of two sources by ~0.62 and 0.59 arcseconds with respect to their positions in previous images available in the literature., Comment: 22 pages, 18 figures, 7 tables. Accepted for publication in A&A

Human label variation (HLV) is a valuable source of information that arises when multiple human annotators provide different labels for valid reasons. In Natural Language Inference (NLI) earlier approaches to capturing HLV involve either collecting annotations from many crowd workers to represent human judgment distribution (HJD) or use expert linguists to provide detailed explanations for their chosen labels. While the former method provides denser HJD information, obtaining it is resource-intensive. In contrast, the latter offers richer textual information but it is challenging to scale up to many human judges. Besides, large language models (LLMs) are increasingly used as evaluators ("LLM judges") but with mixed results, and few works aim to study HJDs. This study proposes to exploit LLMs to approximate HJDs using a small number of expert labels and explanations. Our experiments show that a few explanations significantly improve LLMs' ability to approximate HJDs with and without explicit labels, thereby providing a solution to scale up annotations for HJD. However, fine-tuning smaller soft-label aware models with the LLM-generated model judgment distributions (MJDs) presents partially inconsistent results: while similar in distance, their resulting fine-tuned models and visualized distributions differ substantially. We show the importance of complementing instance-level distance measures with a global-level shape metric and visualization to more effectively evaluate MJDs against human judgment distributions., Comment: Accepted by EMNLP 2024 Findings, 24 pages, 9 figures

Large language models (LLMs) have shown promising abilities as cost-effective and reference-free evaluators for assessing language generation quality. In particular, pairwise LLM evaluators, which compare two generated texts and determine the preferred one, have been employed in a wide range of applications. However, LLMs exhibit preference biases and worrying sensitivity to prompt designs. In this work, we first reveal that the predictive preference of LLMs can be highly brittle and skewed, even with semantically equivalent instructions. We find that fairer predictive preferences from LLMs consistently lead to judgments that are better aligned with humans. Motivated by this phenomenon, we propose an automatic Zero-shot Evaluation-oriented Prompt Optimization framework, ZEPO, which aims to produce fairer preference decisions and improve the alignment of LLM evaluators with human judgments. To this end, we propose a zero-shot learning objective based on the preference decision fairness. ZEPO demonstrates substantial performance improvements over state-of-the-art LLM evaluators, without requiring labeled data, on representative meta-evaluation benchmarks. Our findings underscore the critical correlation between preference fairness and human alignment, positioning ZEPO as an efficient prompt optimizer for bridging the gap between LLM evaluators and human judgments., Comment: EMNLP 2024

This article introduces a simulation platform to study complex crowd behavior in social context. The agent-based model is extended based on the social force model, and it mainly describes how agents interact with each other, and also with surrounding facilities such as walls, doors and exits. The simulation platform is compatible to FDS+Evac, and the input data in FDS+Evac could be imported into our simulation platform to create single-floor compartment geometry, and a flow solver is used to generate the roadmap towards exits. Most importantly, we plan to integrate advanced social and psychological theory into our simulation platform, especially investigating human behavior in emergency evacuation,such as pre-evacuation behavior, exit-selection activities, social group and herding effect and so forth., Comment: 26 pages, 20 figures

The surge of interest in culturally aware and adapted Natural Language Processing (NLP) has inspired much recent research. However, the lack of common understanding of the concept of "culture" has made it difficult to evaluate progress in this emerging area. Drawing on prior research in NLP and related fields, we propose an extensive taxonomy of elements of culture that can provide a systematic framework for analyzing and understanding research progress. Using the taxonomy, we survey existing resources and models for culturally aware and adapted NLP, providing an overview of the state of the art and the research gaps that still need to be filled.

Top-view perspective denotes a typical way in which humans read and reason over different types of maps, and it is vital for localization and navigation of humans as well as of `non-human' agents, such as the ones backed by large Vision-Language Models (VLMs). Nonetheless, spatial reasoning capabilities of modern VLMs remain unattested and underexplored. In this work, we thus study their capability to understand and reason over spatial relations from the top view. The focus on top view also enables controlled evaluations at different granularity of spatial reasoning; we clearly disentangle different abilities (e.g., recognizing particular objects versus understanding their relative positions). We introduce the TopViewRS (Top-View Reasoning in Space) dataset, consisting of 11,384 multiple-choice questions with either realistic or semantic top-view map as visual input. We then use it to study and evaluate VLMs across 4 perception and reasoning tasks with different levels of complexity. Evaluation of 10 representative open- and closed-source VLMs reveals the gap of more than 50% compared to average human performance, and it is even lower than the random baseline in some cases. Although additional experiments show that Chain-of-Thought reasoning can boost model capabilities by 5.82% on average, the overall performance of VLMs remains limited. Our findings underscore the critical need for enhanced model capability in top-view spatial reasoning and set a foundation for further research towards human-level proficiency of VLMs in real-world multimodal tasks., Comment: 9 pages, 3 figures, 3 tables (21 pages, 4 figures, 15 tables including references and appendices)

Large language models (LLMs) often exhibit undesirable behaviours, such as generating untruthful or biased content. Editing their internal representations has been shown to be effective in mitigating such behaviours on top of the existing alignment methods. We propose a novel inference-time editing method, namely spectral editing of activations (SEA), to project the input representations into directions with maximal covariance with the positive demonstrations (e.g., truthful) while minimising covariance with the negative demonstrations (e.g., hallucinated). We also extend our method to non-linear editing using feature functions. We run extensive experiments on benchmarks concerning truthfulness and bias with six open-source LLMs of different sizes and model families. The results demonstrate the superiority of SEA in effectiveness, generalisation to similar tasks, as well as computation and data efficiency. We also show that SEA editing only has a limited negative impact on other model capabilities., Comment: 24 pages, NeurIPS 2024

We consider the first order $q$-difference equation \begin{equation}\tag{\dag} f(qz)^n=R(z,f), \end{equation} where $q\not=0,1$ is a constant and $R(z,f)$ is rational in both arguments. When $|q|\not=1$, we show that, if $(\dag)$ has a zero order transcendental meromorphic solution, then $(\dag)$ reduces to a $q$-difference linear or Riccati equation, or to an equation that can be transformed to a $q$-difference Riccati equation. In the autonomous case, explicit meromorphic solutions of $(\dag)$ are presented. Given that $(\dag)$ can be transformed into a difference equation, we proceed to discuss the growth of the composite function $f(\omega(z))$, where $\omega(z)$ is an entire function satisfying $\omega(z+1)=q\omega(z)$, and demonstrate how the proposed difference Painlev\'e property, as discussed in the literature, applies for $q$-difference equations., Comment: 13 pages

Traditional recommender systems such as matrix factorization methods have primarily focused on learning a shared dense embedding space to represent both items and user preferences. Subsequently, sequence models such as RNN, GRUs, and, recently, Transformers have emerged and excelled in the task of sequential recommendation. This task requires understanding the sequential structure present in users' historical interactions to predict the next item they may like. Building upon the success of Large Language Models (LLMs) in a variety of tasks, researchers have recently explored using LLMs that are pretrained on vast corpora of text for sequential recommendation. To use LLMs for sequential recommendation, both the history of user interactions and the model's prediction of the next item are expressed in text form. We propose CALRec, a two-stage LLM finetuning framework that finetunes a pretrained LLM in a two-tower fashion using a mixture of two contrastive losses and a language modeling loss: the LLM is first finetuned on a data mixture from multiple domains followed by another round of target domain finetuning. Our model significantly outperforms many state-of-the-art baselines (+37% in Recall@1 and +24% in NDCG@10) and our systematic ablation studies reveal that (i) both stages of finetuning are crucial, and, when combined, we achieve improved performance, and (ii) contrastive alignment is effective among the target domains explored in our experiments., Comment: RecSys 2024 (Long Paper)

We prove that if a graph contains the complete bipartite graph $K_{134, 12}$ as an induced minor, then it contains a cycle of length at most~12 or a theta as an induced subgraph. With a longer and more technical proof, we prove that if a graph contains $K_{3, 4}$ as an induced minor, then it contains a triangle or a theta as an induced subgraph. Here, a \emph{theta} is a graph made of three internally vertex-disjoint chordless paths $P_1 = a \dots b$, $P_2 = a \dots b$, $P_3 = a \dots b$, each of length at least two, such that no edges exist between the paths except the three edges incident to $a$ and the three edges incident to $b$. A consequence is that excluding a grid and a complete bipartite graph as induced minors is not enough to guarantee a bounded tree-independence number, or even that the treewidth is bounded by a function of the size of the maximum clique, because the existence of graphs with large treewidth that contain no triangles or thetas as induced subgraphs is already known (the so-called layered wheels)., Comment: 25 pages, 12 figures

In prior work, Gupta et al. (SPAA 2022) presented a distributed algorithm for multiplying sparse $n \times n$ matrices, using $n$ computers. They assumed that the input matrices are uniformly sparse--there are at most $d$ non-zeros in each row and column--and the task is to compute a uniformly sparse part of the product matrix. The sparsity structure is globally known in advance (this is the supported setting). As input, each computer receives one row of each input matrix, and each computer needs to output one row of the product matrix. In each communication round each computer can send and receive one $O(\log n)$-bit message. Their algorithm solves this task in $O(d^{1.907})$ rounds, while the trivial bound is $O(d^2)$. We improve on the prior work in two dimensions: First, we show that we can solve the same task faster, in only $O(d^{1.832})$ rounds. Second, we explore what happens when matrices are not uniformly sparse. We consider the following alternative notions of sparsity: row-sparse matrices (at most $d$ non-zeros per row), column-sparse matrices, matrices with bounded degeneracy (we can recursively delete a row or column with at most $d$ non-zeros), average-sparse matrices (at most $dn$ non-zeros in total), and general matrices.

We continue classification of finite groups which can be used as symmetry group of the scalar sector of the four-Higgs-doublet model (4HDM). Our objective is to systematically construct non-abelian groups via the group extension procedure, starting from the abelian groups $A$ and their automorphism groups $\mathrm{Aut}(A)$. Previously, we considered all cyclic groups $A$ available for the 4HDM scalar sector. Here, we further develop the method and apply it to extensions by the remaining rephasing groups $A$, namely $A = \mathbb{Z_2}\times\mathbb{Z_2}$, $\mathbb{Z_4}\times \mathbb{Z_2}$, and $\mathbb{Z_2}\times \mathbb{Z_2}\times \mathbb{Z_2}$. As $\mathrm{Aut}(A)$ grows, the procedure becomes more laborious, but we prove an isomorphism theorem which helps classify all the options. We also comment on what remains to be done to complete the classification of all finite non-abelian groups realizable in the 4HDM scalar sector without accidental continuous symmetries., Comment: 27 pages, 0 figures, 4 tables. v2: extra clarifications, matches the published version

Context. Gravitational microlensing is a method that is used to discover planet-hosting systems at distances of several kiloparsec in the Galactic disk and bulge. We present the analysis of a microlensing event reported by the Gaia photometric alert team that might have a bright lens. Aims. In order to infer the mass and distance to the lensing system, the parallax measurement at the position of Gaia21blx was used. In this particular case, the source and the lens have comparable magnitudes and we cannot attribute the parallax measured by Gaia to the lens or source alone. Methods. Since the blending flux is important, we assumed that the Gaia parallax is the flux-weighted average of the parallaxes of the lens and source. Combining this assumption with the information from the microlensing models and the finite source effects we were able to resolve all degeneracies and thus obtained the mass, distance, luminosities and projected kinematics of the binary lens and the source. Results. According to the best model, the lens is a binary system at $2.18 \pm 0.07$ kpc from Earth. It is composed of a G star with $0.95\pm 0.17\,M_{\odot}$ and a K star with $0.53 \pm 0.07 \, M_{\odot}$. The source is likely to be an F subgiant star at $2.38 \pm 1.71$ kpc with a mass of $1.10 \pm 0.18 \, M_{\odot}$. Both lenses and the source follow the kinematics of the thin-disk population. We also discuss alternative models, that are disfavored by the data or by prior expectations, however., Comment: 11 pages, 6 figures. Accepted for publication in A&A

We study the following Independent Stable Set problem. Let G be an undirected graph and M = (V(G),I) be a matroid whose elements are the vertices of G. For an integer k\geq 1, the task is to decide whether G contains a set S\subseteq V(G) of size at least k which is independent (stable) in G and independent in M. This problem generalizes several well-studied algorithmic problems, including Rainbow Independent Set, Rainbow Matching, and Bipartite Matching with Separation. We show that - When the matroid M is represented by the independence oracle, then for any computable function f, no algorithm can solve Independent Stable Set using f(k)n^{o(k)} calls to the oracle. - On the other hand, when the graph G is of degeneracy d, then the problem is solvable in time O((d+1)^kn), and hence is FPT parameterized by d+k. Moreover, when the degeneracy d is a constant (which is not a part of the input), the problem admits a kernel polynomial in k. More precisely, we prove that for every integer d\geq 0, the problem admits a kernelization algorithm that in time n^{O(d)} outputs an equivalent framework with a graph on dk^{O(d)} vertices. A lower bound complements this when d is part of the input: Independent Stable Set does not admit a polynomial kernel when parameterized by k+d unless NP \subseteq coNP/poly. This lower bound holds even when M is a partition matroid. - Another set of results concerns the scenario when the graph G is chordal. In this case, our computational lower bound excludes an FPT algorithm when the input matroid is given by its independence oracle. However, we demonstrate that Independent Stable Set can be solved in 2^{O(k)}||M||^{O(1)} time when M is a linear matroid given by its representation. In the same setting, Independent Stable Set does not have a polynomial kernel when parameterized by k unless NP\subseteq coNP/poly., Comment: The full version of a paper accepted for SWAT 2024

We give an algorithm that, given graphs $G$ and $H$, tests whether $H$ is a minor of $G$ in time ${\cal O}_H(n^{1+o(1)})$; here, $n$ is the number of vertices of $G$ and the ${\cal O}_H(\cdot)$-notation hides factors that depend on $H$ and are computable. By the Graph Minor Theorem, this implies the existence of an $n^{1+o(1)}$-time membership test for every minor-closed class of graphs. More generally, we give an ${\cal O}_{H,|X|}(m^{1+o(1)})$-time algorithm for the rooted version of the problem, in which $G$ comes with a set of roots $X\subseteq V(G)$ and some of the branch sets of the sought minor model of $H$ are required to contain prescribed subsets of $X$; here, $m$ is the total number of vertices and edges of $G$. This captures the Disjoint Paths problem, for which we obtain an ${\cal O}_{k}(m^{1+o(1)})$-time algorithm, where $k$ is the number of terminal pairs. For all the mentioned problems, the fastest algorithms known before are due to Kawarabayashi, Kobayashi, and Reed [JCTB 2012], and have a time complexity that is quadratic in the number of vertices of $G$. Our algorithm has two main ingredients: First, we show that by using the dynamic treewidth data structure of Korhonen, Majewski, Nadara, Pilipczuk, and Soko{\l}owski [FOCS 2023], the irrelevant vertex technique of Robertson and Seymour can be implemented in almost-linear time on apex-minor-free graphs. Then, we apply the recent advances in almost-linear time flow/cut algorithms to give an almost-linear time implementation of the recursive understanding technique, which effectively reduces the problem to apex-minor-free graphs., Comment: 81 pages

Large Language Models (LLMs) have demonstrated promising capabilities as automatic evaluators in assessing the quality of generated natural language. However, LLMs still exhibit biases in evaluation and often struggle to generate coherent evaluations that align with human assessments. In this work, we first conduct a systematic study of the misalignment between LLM evaluators and human judgement, revealing that existing calibration methods aimed at mitigating biases are insufficient for effectively aligning LLM evaluators. Inspired by the use of preference data in RLHF, we formulate the evaluation as a ranking problem and introduce Pairwise-preference Search (PairS), an uncertainty-guided search method that employs LLMs to conduct pairwise comparisons and efficiently ranks candidate texts. PairS achieves state-of-the-art performance on representative evaluation tasks and demonstrates significant improvements over direct scoring. Furthermore, we provide insights into the role of pairwise preference in quantifying the transitivity of LLMs and demonstrate how PairS benefits from calibration., Comment: This paper has been accepted by COLM 2024

1. Joint species distribution models (JSDMs) have gained considerable traction among ecologists over the past decade, due to their capacity to answer a wide range of questions at both the species- and the community-level. The family of generalized linear latent variable models in particular has proven popular for building JSDMs, being able to handle many response types including presence-absence data, biomass, overdispersed and/or zero-inflated counts. 2. We extend latent variable models to handle percent cover data, with vegetation, sessile invertebrate, and macroalgal cover data representing the prime examples of such data arising in community ecology. 3. Sparsity is a commonly encountered challenge with percent cover data. Responses are typically recorded as percentages covered per plot, though some species may be completely absent or present, i.e., have 0% or 100% cover respectively, rendering the use of beta distribution inadequate. 4. We propose two JSDMs suitable for percent cover data, namely a hurdle beta model and an ordered beta model. We compare the two proposed approaches to a beta distribution for shifted responses, transformed presence-absence data, and an ordinal model for percent cover classes. Results demonstrate the hurdle beta JSDM was generally the most accurate at retrieving the latent variables and predicting ecological percent cover data.

Markov networks are probabilistic graphical models that employ undirected graphs to depict conditional independence relationships among variables. Our focus lies in constraint-based structure learning, which entails learning the undirected graph from data through the execution of conditional independence tests. We establish theoretical limits concerning two critical aspects of constraint-based learning of Markov networks: the number of tests and the sizes of the conditioning sets. These bounds uncover an exciting interplay between the structural properties of the graph and the amount of tests required to learn a Markov network. The starting point of our work is that the graph parameter maximum pairwise connectivity, $\kappa$, that is, the maximum number of vertex-disjoint paths connecting a pair of vertices in the graph, is responsible for the sizes of independence tests required to learn the graph. On one hand, we show that at least one test with the size of the conditioning set at least $\kappa$ is always necessary. On the other hand, we prove that any graph can be learned by performing tests of size at most $\kappa$. This completely resolves the question of the minimum size of conditioning sets required to learn the graph. When it comes to the number of tests, our upper bound on the sizes of conditioning sets implies that every $n$-vertex graph can be learned by at most $n^{\kappa}$ tests with conditioning sets of sizes at most $\kappa$. We show that for any upper bound $q$ on the sizes of the conditioning sets, there exist graphs with $O(n q)$ vertices that require at least $n^{\Omega(\kappa)}$ tests to learn. This lower bound holds even when the treewidth and the maximum degree of the graph are at most $\kappa+2$. On the positive side, we prove that every graph of bounded treewidth can be learned by a polynomial number of tests with conditioning sets of sizes at most $2\kappa$., Comment: AISTATS 2024

Supervised fine-tuning (SFT), supervised instruction tuning (SIT) and in-context learning (ICL) are three alternative, de facto standard approaches to few-shot learning. ICL has gained popularity recently with the advent of LLMs due to its simplicity and sample efficiency. Prior research has conducted only limited investigation into how these approaches work for multilingual few-shot learning, and the focus so far has been mostly on their performance. In this work, we present an extensive and systematic comparison of the three approaches, testing them on 6 high- and low-resource languages, three different NLU tasks, and a myriad of language and domain setups. Importantly, performance is only one aspect of the comparison, where we also analyse the approaches through the optics of their computational, inference and financial costs. Our observations show that supervised instruction tuning has the best trade-off between performance and resource requirements. As another contribution, we analyse the impact of target language adaptation of pretrained LLMs and find that the standard adaptation approaches can (superficially) improve target language generation capabilities, but language understanding elicited through ICL does not improve and remains limited, with low scores especially for low-resource languages.

We give an algorithm that given a graph $G$ with $n$ vertices and $m$ edges and an integer $k$, in time $O_k(n^{1+o(1)}) + O(m)$ either outputs a rank decomposition of $G$ of width at most $k$ or determines that the rankwidth of $G$ is larger than $k$; the $O_k(\cdot)$-notation hides factors depending on $k$. Our algorithm returns also a $(2^{k+1}-1)$-expression for cliquewidth, yielding a $(2^{k+1}-1)$-approximation algorithm for cliquewidth with the same running time. This improves upon the $O_k(n^2)$ time algorithm of Fomin and Korhonen [STOC 2022]. The main ingredient of our algorithm is a fully dynamic algorithm for maintaining rank decompositions of bounded width: We give a data structure that for a dynamic $n$-vertex graph $G$ that is updated by edge insertions and deletions maintains a rank decomposition of $G$ of width at most $4k$ under the promise that the rankwidth of $G$ never grows above $k$. The amortized running time of each update is $O_k(2^{\sqrt{\log n} \log \log n})$. The data structure furthermore can maintain whether $G$ satisfies some fixed ${\sf CMSO}_1$ property within the same running time. We also give a framework for performing ``dense'' edge updates inside a given set of vertices $X$, where the new edges inside $X$ are described by a given ${\sf CMSO}_1$ sentence and vertex labels, in amortized $O_k(|X| \cdot 2^{\sqrt{\log n} \log \log n})$ time. Our dynamic algorithm generalizes the dynamic treewidth algorithm of Korhonen, Majewski, Nadara, Pilipczuk, and Soko{\l}owski [FOCS 2023].

Recent work has shown that, while large language models (LLMs) demonstrate strong word translation or bilingual lexicon induction (BLI) capabilities in few-shot setups, they still cannot match the performance of 'traditional' mapping-based approaches in the unsupervised scenario where no seed translation pairs are available, especially for lower-resource languages. To address this challenge with LLMs, we propose self-augmented in-context learning (SAIL) for unsupervised BLI: starting from a zero-shot prompt, SAIL iteratively induces a set of high-confidence word translation pairs for in-context learning (ICL) from an LLM, which it then reapplies to the same LLM in the ICL fashion. Our method shows substantial gains over zero-shot prompting of LLMs on two established BLI benchmarks spanning a wide range of language pairs, also outperforming mapping-based baselines across the board. In addition to achieving state-of-the-art unsupervised BLI performance, we also conduct comprehensive analyses on SAIL and discuss its limitations., Comment: ACL 2024 Main Conference; 11 Pages, 3 Figures, 9 Tables

Objective This study investigates what kind of conceptions primary school students have about ML if they are not conceptually "primed" with the idea that in ML, humans teach computers. Method Qualitative survey responses from 197 Finnish primary schoolers were analyzed via an abductive method. Findings We identified three partly overlapping ML conception categories, starting from the most accurate one: ML is about teaching machines (34%), ML is about coding (7.6%), and ML is about learning via or about machines (37.1%). Implications The findings suggest that without conceptual clues, children's conceptions of ML are varied and may include misconceptions such as ML is about learning via or about machines. The findings underline the importance of clear and systematic use of key concepts in computer science education. Besides researchers, this study offers insights for teachers, teacher educators, curriculum developers, and policymakers. Method Qualitative survey responses from 197 Finnish primary schoolers were analyzed via an abductive method. Findings We identified three partly overlapping ML conception categories, starting from the most accurate one: ML is about teaching machines (34%), ML is about coding (7.6%), and ML is about learning via or about machines (37.1%). Implications The findings suggest that without conceptual clues, children's conceptions of ML are varied and may include misconceptions such as ML is about learning via or about machines. The findings underline the importance of clear and systematic use of key concepts in computer science education. Besides researchers, this study offers insights for teachers, teacher educators, curriculum developers, and policymakers.

In recent years, informationally complete measurements have attracted considerable attention, especially in the context of classical shadows. In the particular case of informationally over-complete measurements, for which the number of possible outcomes exceeds the dimension of the space of linear operators in Hilbert space, the dual POVM operators used to interpret the measurement outcomes are not uniquely defined. In this work, we propose a method to optimize the dual operators after the measurements have been carried out in order to produce sharper, unbiased estimations of observables of interest. We discuss how this procedure can produce zero-variance estimations in cases where the classical shadows formalism, which relies on so-called canonical duals, incurs exponentially large measurement overheads. We also analyze the algorithm in the context of quantum simulation with randomized Pauli measurements, and show that it can significantly reduce statistical errors with respect to canonical duals on multiple observable estimations.

Large Language Models (LLMs) are difficult to fully fine-tune (e.g., with instructions or human feedback) due to their sheer number of parameters. A family of parameter-efficient sparse fine-tuning methods have proven promising in terms of performance but their memory requirements increase proportionally to the size of the LLMs. In this work, we scale sparse fine-tuning to state-of-the-art LLMs like LLaMA 2 7B and 13B. We propose SpIEL, a novel sparse fine-tuning method which, for a desired density level, maintains an array of parameter indices and the deltas of these parameters relative to their pretrained values. It iterates over: (a) updating the active deltas, (b) pruning indices (based on the change of magnitude of their deltas) and (c) regrowth of indices. For regrowth, we explore two criteria based on either the accumulated gradients of a few candidate parameters or their approximate momenta estimated using the efficient SM3 optimizer. We experiment with instruction-tuning of LLMs on standard dataset mixtures, finding that SpIEL is often superior to popular parameter-efficient fine-tuning methods like LoRA (low-rank adaptation) in terms of performance and comparable in terms of run time. We additionally show that SpIEL is compatible with both quantization and efficient optimizers, to facilitate scaling to ever-larger model sizes. We release the code for SpIEL at https://github.com/AlanAnsell/peft and for the instruction-tuning experiments at https://github.com/ducdauge/sft-llm.

With technology for digital photography and high resolution displays rapidly evolving and gaining popularity, there is a growing demand for blind image quality assessment (BIQA) models for high resolution images. Unfortunately, the publicly available large scale image quality databases used for training BIQA models contain mostly low or general resolution images. Since image resizing affects image quality, we assume that the accuracy of BIQA models trained on low resolution images would not be optimal for high resolution images. Therefore, we created a new high resolution image quality database (HRIQ), consisting of 1120 images with resolution of 2880x2160 pixels. We conducted a subjective study to collect the subjective quality ratings for HRIQ in a controlled laboratory setting, resulting in accurate MOS at high resolution. To demonstrate the importance of a high resolution image quality database for training BIQA models to predict mean opinion scores (MOS) of high resolution images accurately, we trained and tested several traditional and deep learning based BIQA methods on different resolution versions of our database. The database is publicly available in https://github.com/jarikorhonen/hriq.

Tight relationships exist in the local universe between the central stellar properties of galaxies and the mass of their supermassive black hole. These suggest galaxies and black holes co-evolve, with the main regulation mechanism being energetic feedback from accretion onto the black hole during its quasar phase. A crucial question is how the relationship between black holes and galaxies evolves with time; a key epoch to probe this relationship is at the peaks of star formation and black hole growth 8-12 billion years ago (redshifts 1-3). Here we report a dynamical measurement of the mass of the black hole in a luminous quasar at a redshift of 2, with a look back time of 11 billion years, by spatially resolving the broad line region. We detect a 40 micro-arcsecond (0.31 pc) spatial offset between the red and blue photocenters of the H$\alpha$ line that traces the velocity gradient of a rotating broad line region. The flux and differential phase spectra are well reproduced by a thick, moderately inclined disk of gas clouds within the sphere of influence of a central black hole with a mass of 3.2x10$^{8}$ solar masses. Molecular gas data reveal a dynamical mass for the host galaxy of 6x10$^{11}$ solar masses, which indicates an under-massive black hole accreting at a super-Eddington rate. This suggests a host galaxy that grew faster than the supermassive black hole, indicating a delay between galaxy and black hole formation for some systems., Comment: 5 pages Main text, 8 figures, 2 tables, to be published in Nature, under embargo until 29 January 2024 16:00 (London)